Univariate and Multivariate Time Series Predictions

Abstract

AbstractIn this chapter we present the overall framework inside which we develop our quantitative approach to making financial market predictions. This is done by starting with a mathematical formulation of the basic question we face: how do we forecast the future value of a particular asset whose values over a certain period of the past we know? In order to describe the structure of the problem in more quantitative terms we must set out notation for these values, as well of those of other similar assets we also wish to predict at the same time or of economic or other financial data which may be thought to have an influence on the value or values we are trying to predict. We have already set out in the previous chapter reasons why extra variables, the so-called fundamentals, may contain information on the future values of bond or equity prices, so such an approach can have value. Some of the data required may, however, be difficult to obtain or may be of the wrong periodicity. This can happen for economic data in particular, such as overall assessors of the economy of a country, like its GDP, which may only be available quarterly. Thus an alternative is to use only the actual or target series itself, the one being predicted. It may be suggested that a given time series of financial data, such as a series of USA bond values, contains all the requisite information in itself. This is reasonable to argue, since in the past all the effects of other economic or financial data on the target series should be observable in the patterns that may arise in successive target values. Thus the way in which these patterns determine future values should be able to be discerned. Such an extreme approach, neglecting all data but the given time series being predicted, is termed univariate (it depends only on the values of a single series). On the other hand, the use of information arising from other financial or economic time series (called fundamentals or indicator variables) to make the prediction is termed a multivariate approach.KeywordsFinancial AssetMultivariate ApproachTarget SeriesEconomic Time SeriesInput SeriesThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.